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Accelerated algorithms for maximum likelihood image reconstruction are essential for emerging applications such as 3D tomography, dynamic tomographic imaging, and other high dimensional inverse problems. In this paper, we introduce and…
Because diffusion models have shown impressive performances in a number of tasks, such as image synthesis, there is a trend in recent works to prove (with certain assumptions) that these models have strong approximation capabilities. In…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
While the mathematical foundations of score-based generative models are increasingly well understood for unconstrained Euclidean spaces, many practical applications involve data restricted to bounded domains. This paper provides a…
We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…
Evidence-based deep learning represents a burgeoning paradigm for uncertainty estimation, offering reliable predictions with negligible extra computational overheads. Existing methods usually adopt Kullback-Leibler divergence to estimate…
We present a class of algorithms capable of directly training deep neural networks with respect to large families of task-specific performance measures such as the F-measure and the Kullback-Leibler divergence that are structured and…
We examine the estimation of the Kullback-Leibler (KL) divergence and the use of the goodness-of-fit test for multivariate continuous distributions. Our starting point is the maximum entropy principle for Shannon entropy: among all…
We investigate the strong approximation of stochastic differential equations whose drift is square-integrable in time and Dini continuous in space, while the diffusion coefficient is non-constant and uniformly elliptic. Using a refined…
Conventional colorimetric sensing methods typically rely on signal intensity at a single wavelength, often selected heuristically based on peak visual modulation. This approach overlooks the structured information embedded in full-spectrum…
While diffusion models excel at generating high-quality images, prior work reports a significant performance gap between diffusion and autoregressive (AR) methods in language modeling. In this work, we show that simple masked discrete…
Discrete diffusion models offer global context awareness and flexible parallel generation. However, uniform random noise schedulers in standard DLLM training overlook the highly non-uniform information density inherent in real-world…
We study the problem of unbiased estimation of expectations with respect to (w.r.t.) $\pi$ a given, general probability measure on $(\mathbb{R}^d,\mathcal{B}(\mathbb{R}^d))$ that is absolutely continuous with respect to a standard Gaussian…
Knowledge of the mass composition of ultra-high-energy cosmic rays is crucial to understanding their origins; however, current approaches have limited event-by-event resolution. With fluorescence telescope measurements of the longitudinal…
The ongoing technological revolution in measurement systems enables the acquisition of high-resolution samples in fields such as engineering, biology, and medicine. However, these observations are often subject to errors from measurement…
The Diffusion Model has not only garnered noteworthy achievements in the realm of image generation but has also demonstrated its potential as an effective pretraining method utilizing unlabeled data. Drawing from the extensive potential…
This study tackles the efficient estimation of Kullback-Leibler (KL) Divergence in Dirichlet Mixture Models (DMM), crucial for clustering compositional data. Despite the significance of DMMs, obtaining an analytically tractable solution for…
$f$-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler…
We study few-shot debugging of transformer based natural language understanding models, using recently popularized test suites to not just diagnose but correct a problem. Given a few debugging examples of a certain phenomenon, and a…
Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for…